Apple's logo. / Paul Sakuma, AP

by Jon Swartz, USA TODAY

by Jon Swartz, USA TODAY

His tweet today about building a sizable stock stake in Apple, the world's most valuable tech company, sent the company's stock up nearly 5% -- and, perhaps, the blood pressure of executives in Cupertino, Calif., where Apple is based.

"We currently have a large position in Apple," Icahn tweeted, without providing specifics. "We believe the company to be extremely undervalued." (Apple shares are trading just shy of $500.)

"We plan to speak again shortly," wrote Icahn, who added he spoke to Apple CEO Tim Cook.

A civil discussion is positive news for Apple, given Icahn's adamant opposition to Michael Dell and Silver Lake Management LLC in their efforts to take Dell private. Before that, billionaire Icahn collected big chunks of shares in Yahoo and Motorola and sought change.

Icahn's predilection for forcing the issue at tech companies comes at a particularly delicate time for Apple, which is under a withering assault from the likes of Google and Samsung Electronics amid concerns Apple can still produce new hardware hits.

The uncertainty was underscored by Oracle CEO Larry Ellison, who told CBS This Morning's Charlie Rose this week that Apple will languish without its co-founder, the late Steve Jobs. "He was our Picasso," Ellison said. "He was an incredible inventor."

Apple has coped with disgruntled investors like hedge-fund manager David Einhorn, who wanted the company to return some of its hoard of cash to shareholders.

But with the mercurial Icahn, the stakes may be higher -- and far riskier -- as Apple navigates intensified competition and lingering doubts about its future.